Studies are being conducted on methods of designing control systems for controlling repetitive target values under which a tracking error of one period before is utilized (e.g., "Precision Control over the Repetitive Operation of Power Supply for Proton Synchrotron Electromagnet" by Inoue et al, Complied Papers of the Japan Electric Society, Vol. 100. No. 7, etc.). FIG. 28 illustrates the basic concept of such a method, wherein r, e, u and x represent a target value, a tracking error, a control input and a control output, respectively. L designates a period of the target value (see FIG. 29A, whereas e.sup.-Ls is a dead time element which causes a delay by time L. The control input u(t) at time t is given by EQU u(t)=u(t-L)+e(t-L)
and what is featured in this is a control input of one period before and a tracking error of one period before are utilized; advantages claimed therefor include the possibility of not only high precision follow-up but also removal of periodic disturbance.
This method is also applicable to a case where the target value repeats a similar pattern intermittently (see FIG. 29B) and the control input u(t) at time t then becomes EQU u(t)=u(t')+e(t')
where t' represents the time at the preceding trial corresponding to the time t.
There is also a method of the sort disclosed in the present inventor's patent application laid open by Japanese Patent Publication No. 118405/1987 as a predicted control method for minimizing the weighting square sum of the estimated values of a furture tracking error.
In this method, a control input u(i) at present sampling time i is given as follows ##EQU1## using an incremental control input. In this case, a future tracking error consisting of a sampling value of the indicial response of a controlled object, the before incremental control input, the present output and a future target value is estimated and an incremental control input m(i) is determined so that the weighting square sum of the estimated values is minimized.
Since a future target value is utilized in this method, the response characteristics obtained are superior to those obtained from a control system using only the present target value. Further, the advantage is simply that the four fundamental arithmetic operations are needed to implement the method.
Moreover, Japanese Patent Application Laid-Open No. 118406/1987 discloses a proposal of a predicted control method utilizing a tracking error of one trial before, the method being characterized in that a target value repeating the same pattern is provided with a combination of the aforesaid incremental control input and the constant number of times the tracking error of one trial before as a new incremental control input.
However, the above-described design method for the repetitive target value, i.e., the repetitive control method and what is disclosed in Japanese Patent Application Laid-Open No. 118406/1987 both utilize the tracking error at the time of one period before or the tracking error at time t' corresponding to the present time t at the time of the preceding trial (see FIG. 29B. Despite the fact that a tracking error during the period from the time of one period before up to the present or a tracking error after the time t' is extremely useful when the control input at this time is determined, such a tracking error has not been utilized in those methods.